It is known that heating of a constant load, d.c. electric motor cannot be accurately assessed by inserting thermal sensors in it. However, there are special applications in which the causes of motor heating can easily be determined and thus reduced to a formula, having parameters related to the type of motor and method of using it. On the basis of the formula, it is possible at any given time to determine the exact amount of heat produced in the motor. Consequently, rather than inserting thermal sensors in the motor, an electrical circuit which simulates the motor heating in accordance with the appropriate formula is associated with the constant load d.c. motor. Often the electrical value which this circuit supplies for the simulated heating is compared with a given threshold value. When the threshold is reached or exceeded, the motor is stopped until it has cooled sufficiently. The prior art thus includes a wide variety of thermal simulators.